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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009
Exercise 1: General Probability I 09/03/2009
1. In a survey of 120 students, the following data was obtained: 60 took English, 56 took Math, 42 took Chemistry, 34 took English and Math, 20 took Math and Chemistry, 16 took English and Chemistry, 6 took all three subjects. Find the number of students who took (a) (b) (c) (d) none of the subjects, Math, but not English or Chemistry, English and Math but not Chemistry, exactly one subject. 2. Suppose that P [A ∩ B ]=0.2, P [A]=0.6, and P [B ]=0.5. Find P [A ∪ B ], P [A ∩ B ], P [A ∩ B ] and P [A ∪ B ]. 3. Event C is a subevent of A ∪ B . Which of the following must be true? (1) A ∪ C = B ∪ C (2) P [C ] = P [A ∩ C ] + P [B ∩ C ] − P [A ∩ B ∩ C ] (3) A ∩ C ⊂ B (a) All but (1). (b) All but (2). (c) All but (3). (d) (2) only. (e) (3) only. 1 4. A life insurer classies insurance applicants according to the following attributes: M - the applicant is male, H - the applicant is a homeowner. Out of a large number of applicants the insurer has identied the following information: 40% of applicants are male, 40% of applicants are homeowners and 20% of applicants are female homeowners. Find the percentage of applicants who are male and do not own a home. 5. Fred, Ned and Ted each have season tickets to the US Open. Each one of them might, or might not attend any particular game. The probabilities describing their attendance for any particular game are: P [at least one of them attends the game]=0.95, P [at least two of them attend the game]=0.80, and P [all three of them attend the game]=0.50. Their attendance pattern is also symmetric in the following way: P [F ] = P [N ] = P [T ] and P [F ∩ N ] = P [F ∩ T ] = P [N ∩ T ], where F , N and T denote the events that Fred, Ted and Ned attended the game, respectively. For a particular game, nd the probability that Fred and Ned attended. 2 ...
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